Question

If the mid-point of the line segment joining the points A(3, 4) and B(k, 6) is P(x, y) and x + y – 10 = 0, find the value of k.

Answer 1

x + y − 10 = 0

Midpoint = `((x_1 + x_2)/2, (y_1+y_2)/2)`

`(x, y) = ((3 + k)/2, 10/2)`

`(x, y) = ((3 + k)/2, 5)`

`(3 + k)/2 + 5 - 10 = 0`

`(3 + k)/2 = 5`

3 + k = 10

k = 10 – 3

k = 7

Answer 2

Here, `(3 + k)/2 = x`

And `y = (4 + 6)/2` = `10/2` = 5

Given, x + y – 10 = 0

⇒ `(3 + k)/2 + 5 - 10 = 0`

⇒ `(3 + k)/2 = 5`

⇒ 3 + k = 10

⇒ k = 10 – 3

⇒ k = 7